I am looking for non-canonical sorts of lists. A function that would give:
Sort[X, "order type"]
With "order type" being colex, revlex, etc.
I believe you can effect any of the lex, colex, revlex, revcolex sorts by reversing elements and lists in the proper sequence.
Edit: My original answer used
The simplest variation, merely reverse the list after sorting:
Reverse the elements before sorting, using
Simply reverse the entire list in addition to the steps for the colex sort:
A visualization function:
A random shuffle of subsets:
A comparative graphic: